QuadSim — Quadrupole Ion Filter Simulator

Operating point

RF amplitude V 404 V

U / V ratio 0.102

RF frequency Ω/2π 1.00 MHz

Rod field radius r₀ 3.0 mm

Ions injected

Test m/z values (comma-separated)

Ion injection energy 5 eV

Quadrupole length 200 mm

Simulation speed 0.50×

Legend

Operating values

U (DC)
41.7 V

a (m/z 500)
0.234

V (RF)
250 V

q (m/z 500)
0.706

How it works

Two opposing rod pairs carry +(U − V cos Ωt) and −(U − V cos Ωt). The resulting hyperbolic potential gives ions a Mathieu equation in x and y. Whether the trajectory stays bounded depends only on the dimensionless parameters a = 8eU / (m r₀² Ω²) and q = 4eV / (m r₀² Ω²). Operating near the apex of the stability region transmits a narrow m/z window.

End-on view (x–y cross section)

+(U − V cos Ωt) rods −(U − V cos Ωt) rods

Mathieu stability diagram (a–q)

stable region scan line a/q = 2U/V

Side view — ions traveling down the quadrupole (z axis)

solid trace = x displacement dashed trace = y displacement